A presheaf is a functor from a category of open sets of a topological space to another category, usually the category of sets or abelian groups, that assigns to each open set a set of 'sections' over that open set. It allows for the systematic way of collecting local data about a space, which can then be patched together to study global properties. The concept is foundational in the study of sheaves and sheaf cohomology, facilitating the transition from local to global analysis.
congrats on reading the definition of presheaf. now let's actually learn it.